Model 1: Symmetric Learning¶
This is a standard RLDDM model. The model assumes that participants update expected values between two doors according to a simple Rescorla-Wagner updating rule. Choices are made over these expected values according to a logistic softmax function, with a temperature parameter that reflects sensitivity to noise. Response times are assumed to be sampled from a Wiener first passage time distribution with parameters reflecting boundary separation (emphasis on speed or accuracy), the rate of evidence accumulation, initial bias, and non-decision time. The rate of evidence accumulation is assumed to be a weighted difference between expected values.
Parameters¶
alpha = boundary separation (as $\alpha \rightarrow \infty$, accuracy increases at the cost of speed; hesitancy)
beta = initial bias (should be around $0$ for no bias; $\beta > 0.5$ is bias toward the exploitative door)
deltac = drift rate scalar (as $\delta c \rightarrow \infty$, differences between expected values are more weighted as evidence for a decision)
tau = non-decision time (proportion of response time, in seconds, that does not reflect decision-making)
A = learning-rate (as $A \rightarrow 1$, updating is more reactive to reward prediction errors; larger swings)
B = inverse sensitivity to noise (as $B \rightarrow \infty$, choice becomes more deterministic or exploitative)
Model 2: Asymmetric Learning¶
This is identical to Model 1 except that it uses separate learning-rates for positive and negative feedback.
Additional Parameters¶
Ap = learning-rate to positive feedback
An = learning-rate to negative feedback
Model Comparison¶
Here we compare point-wise out-of-sample predictive accuracy between models (Vehtari et al., 2017). This is accomplished by computing leave-one-out cross-validation scores using Pareto smoothed importance sampling. Cross-validation scores reflect expected log point-wise predictive densities weighted with penalty terms controlling for both a model’s goodness of fit to the data and the complexity of the model.
Higher loo means better fit. Here, we see that the symmetric model better fits the data.
In [242]:
compdf = az.compare({'asymmetric': azdf1, 'symmetric': azdf2}, ic='loo')
compdf
Out[242]:
| rank | loo | p_loo | d_loo | weight | se | dse | warning | loo_scale | |
|---|---|---|---|---|---|---|---|---|---|
| symmetric | 0 | -668.754513 | 94.073852 | 0.0 | NaN | 818.34113 | 0.0 | True | log |
| asymmetric | 1 | -5005.142643 | 3179.161037 | 4336.38813 | 0.0 | 149.240192 | 895.248201 | True | log |
In [239]:
az.plot_compare(compdf)
Out[239]:
<AxesSubplot:xlabel='Log'>
Symmetric Model: Parameter Correlations¶
Here, we check the correlation between parameters in the Happy, Sad, Angry, Desire, and Neutral conditions. Correlation between parameters posteriors can indicate interdependence during sampling. If we have interdependence, it can be difficult to make inferences about effects of condition. For example, a low learning-rate and high noise sensitivity in the Happy condition can lead to the same likelihood as a high learning-rate and low noise sensitivity in that same group; what we estimated could be happenstance.
What do we find?¶
We do find that some parameters are correlated, such as drift-rate scalar and noise sensitivity (which makes sense, considering that we'd expect a more exploitative person would be more likely to consider expected value differences as evidence). That said, we must be careful when making inferences about correlated parameters such as these. For example, if we estimate both of these parameters to be high in, say, the Happy group, it could be just as likely in reality that they are both low in that group, and our sampler simply converged on the high values by happenstance. We'll want to do more robust parameter recovery as a sanity check later. For now, we'll consider our parameter estimates accurate.
In [327]:
plot_paramcorr(df1, paramsearch(df1), ['Happy', 'Sad', 'Angry', 'Desire', 'Neutral'])
Asymmetric Model: Parameter Correlations¶
Let's run the same correlations for the Asymmetric Model.
What do we find?¶
The parameters are slightly less correlated, which is good for inference. We can also see now that the negative correlation between learning-rate and noise sensitivity in the Symmetric Model is mostly due to learning from positive feedback. Maybe people aren't learning much from negative feedback on this task?
In [328]:
plot_paramcorr(df2, paramsearch(df2), ['Happy', 'Sad', 'Angry', 'Desire', 'Neutral'])
Symmetric Model: Happy vs. Neutral¶
Alpha - Boundary Separation¶
Happy condition had a smaller boundary separation than Neutral condition. This suggests that people in the Happy condition focused more on speed than accuracy.
Beta - Initial Bias¶
Happy condition had an equivalent bias as Neutral condition.
Deltac - Drift-Rate Scalar¶
Happy condition had an equivalent weight of EV differences on drift-rate as Neutral condition.
Tau - Non-Decision Time¶
Happy condition had a shorter non-decision time than Neutral condition. This is about 45 milliseconds difference, so it's probably not meaningful.
A - Learning-Rate¶
Happy condition had a smaller learning-rate than Neutral condition.
B - Inverse Noise Sensitivity¶
Happy condition had an equivalent inverse noise sensitivity as Neutral condition.
In [337]:
bayeseffect(df1, 'alpha', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Happy', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.016 H0 Odds: 0.32 H1 Odds: 1.035 There is 223.227% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 3.232 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.26 H0 Odds: 5.234 H1 Odds: 0.779 There is 571.869% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.149 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.167 H0 Odds: 3.366 H1 Odds: 0.877 There is 283.975% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.26 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0 H0 Odds: 0.0 H1 Odds: 1.052 There is 95682789430.198% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 956827895.302 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.007 H0 Odds: 0.144 H1 Odds: 1.045 There is 625.765% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 7.258 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.178 H0 Odds: 3.595 H1 Odds: 0.865 There is 315.777% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.241 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Symmetric Model: Sad vs. Neutral¶
Alpha - Boundary Separation¶
Sad condition had a slightly larger boundary separation than Neutral condition, but not enough to be considered significant. If this effect were greater, it would suggest that people in the Sad condition focused more on accuracy than speed.
Beta - Initial Bias¶
Sad condition had an equivalent bias as Neutral condition.
Deltac - Drift-Rate Scalar¶
Sad condition had a slightly larger weight of EV differences on drift-rate than Neutral condition, but not enough to be considered significant. If this effect were greater, it would suggest that people in the Sad condition used EV differences more as evidence.
Tau - Non-Decision Time¶
Sad condition had a shorter non-decision time than Neutral condition. This is about 25 milliseconds difference, so it's probably not meaningful.
A - Learning-Rate¶
Sad condition had a smaller learning-rate than Neutral condition.
B - Inverse Noise Sensitivity¶
Sad condition had a slightly larger inverse noise sensitivity than Neutral condition, but not enough to be considered significant. If this effect were greater, it would suggest that people in the Sad condition were more exploitative.
In [338]:
bayeseffect(df1, 'alpha', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Sad', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.044 H0 Odds: 0.89 H1 Odds: 1.006 There is 12.979% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.13 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.254 H0 Odds: 5.126 H1 Odds: 0.785 There is 553.292% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.153 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.036 H0 Odds: 0.717 H1 Odds: 1.015 There is 41.537% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.415 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0 H0 Odds: 0.0 H1 Odds: 1.052 There is 2539156.405% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 25392.564 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.001 H0 Odds: 0.019 H1 Odds: 1.051 There is 5534.732% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 56.347 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.084 H0 Odds: 1.695 H1 Odds: 0.964 There is 75.848% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.569 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Symmetric Model: Angry vs. Neutral¶
Alpha - Boundary Separation¶
Angry condition had a larger boundary separation than Neutral condition. This suggests that people in the Angry condition focused more on accuracy than speed.
Beta - Initial Bias¶
Angry condition had an equivalent bias as Neutral condition.
Deltac - Drift-Rate Scalar¶
Angry condition had an equivalent weight of EV differences on drift-rate as Neutral condition.
Tau - Non-Decision Time¶
Angry condition had an equivalent non-decision time as Neutral condition.
A - Learning-Rate¶
Angry condition had a smaller learning-rate than Neutral condition.
B - Inverse Noise Sensitivity¶
Angry condition had an equivalent inverse noise sensitivity as Neutral condition.
In [339]:
bayeseffect(df1, 'alpha', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Angry', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.004 H0 Odds: 0.086 H1 Odds: 1.048 There is 1111.49% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 12.115 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.265 H0 Odds: 5.335 H1 Odds: 0.774 There is 589.498% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.145 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.239 H0 Odds: 4.819 H1 Odds: 0.801 There is 501.899% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.166 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.154 H0 Odds: 3.109 H1 Odds: 0.89 There is 249.319% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.286 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.016 H0 Odds: 0.314 H1 Odds: 1.036 There is 230.207% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 3.302 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.23 H0 Odds: 4.626 H1 Odds: 0.811 There is 470.689% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.175 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Symmetric Model: Desire vs. Neutral¶
Alpha - Boundary Separation¶
Desire condition had a larger boundary separation than Neutral condition. This suggests that people in the Desire condition focused more on accuracy than speed.
Beta - Initial Bias¶
Desire condition had an equivalent bias as Neutral condition.
Deltac - Drift-Rate Scalar¶
Desire condition had an equivalent weight of EV differences on drift-rate as Neutral condition.
Tau - Non-Decision Time¶
Desire condition had a longer non-decision time than Neutral condition. This is about 40 milliseconds difference, so it's probably not meaningful.
A - Learning-Rate¶
Desire condition had an equivalent learning-rate as Neutral condition.
B - Inverse Noise Sensitivity¶
Desire condition had an equivalent inverse noise sensitivity as Neutral condition.
In [340]:
bayeseffect(df1, 'alpha', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'beta', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'deltac', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'tau', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'A', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df1, 'B', 'Desire', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.009 H0 Odds: 0.188 H1 Odds: 1.042 There is 455.242% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 5.552 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.296 H0 Odds: 5.968 H1 Odds: 0.741 There is 705.872% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.124 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.248 H0 Odds: 5.005 H1 Odds: 0.791 There is 532.738% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.158 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0 H0 Odds: 0.0 H1 Odds: 1.052 There is 290185305.198% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 2901854.052 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.198 H0 Odds: 3.996 H1 Odds: 0.844 There is 373.656% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.211 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.24 H0 Odds: 4.843 H1 Odds: 0.799 There is 505.819% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.165 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Asymmetric Model: Contrasts¶
Here, I will display all contrasts for the asymmetric model. Since it is not the winning model, I will not draw inferences from the contrasts, but will report those contrasts for completeness. Recall that Ap is the learning-rate for positive feedback and An is for negative feedback.
In [341]:
bayeseffect(df2, 'alpha', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Happy', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'alpha', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Sad', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'alpha', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Angry', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'alpha', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'beta', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'deltac', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'tau', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'Ap', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'An', 'Desire', 'Neutral', 0.8, 0.95)
bayeseffect(df2, 'B', 'Desire', 'Neutral', 0.8, 0.95)
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.01 H0 Odds: 0.205 H1 Odds: 1.041 There is 407.035% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 5.07 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.219 H0 Odds: 4.406 H1 Odds: 0.822 There is 435.865% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.187 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.169 H0 Odds: 3.404 H1 Odds: 0.875 There is 289.211% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.257 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0 H0 Odds: 0.0 H1 Odds: 1.052 There is 1091642010.626% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 10916421.106 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.012 H0 Odds: 0.248 H1 Odds: 1.039 There is 318.262% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 4.183 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.054 H0 Odds: 1.092 H1 Odds: 0.995 There is 9.729% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.911 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.152 H0 Odds: 3.07 H1 Odds: 0.892 There is 244.181% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.291 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.026 H0 Odds: 0.533 H1 Odds: 1.024 There is 92.167% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.922 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.188 H0 Odds: 3.786 H1 Odds: 0.855 There is 342.967% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.226 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.026 H0 Odds: 0.523 H1 Odds: 1.025 There is 95.898% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.959 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0 H0 Odds: 0.0 H1 Odds: 1.052 There is 1469043.763% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 14691.438 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.031 H0 Odds: 0.626 H1 Odds: 1.02 There is 62.755% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.628 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.001 H0 Odds: 0.028 H1 Odds: 1.051 There is 3631.519% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 37.315 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.061 H0 Odds: 1.235 H1 Odds: 0.988 There is 25.055% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.8 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.004 H0 Odds: 0.076 H1 Odds: 1.048 There is 1272.845% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 13.728 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.284 H0 Odds: 5.732 H1 Odds: 0.753 There is 661.184% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.131 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.221 H0 Odds: 4.458 H1 Odds: 0.819 There is 443.97% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.184 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.162 H0 Odds: 3.263 H1 Odds: 0.882 There is 270.012% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.27 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.013 H0 Odds: 0.263 H1 Odds: 1.038 There is 295.569% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 3.956 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.033 H0 Odds: 0.664 H1 Odds: 1.018 There is 53.231% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.532 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.213 H0 Odds: 4.295 H1 Odds: 0.828 There is 418.723% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.193 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.003 H0 Odds: 0.059 H1 Odds: 1.049 There is 1667.51% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 17.675 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.301 H0 Odds: 6.064 H1 Odds: 0.736 There is 724.397% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.121 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.259 H0 Odds: 5.223 H1 Odds: 0.78 There is 569.945% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.149 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.0 H0 Odds: 0.0 H1 Odds: 1.052 There is 332936956.811% more evidence for the alternative hypothesis than the null for an effect at 0.8 Evidence satisfactory for conclusions. There is STRONG evidence that there IS an effect of 0.8 BF: 3329370.568 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.177 H0 Odds: 3.567 H1 Odds: 0.866 There is 311.866% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.243 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.042 H0 Odds: 0.845 H1 Odds: 1.008 There is 19.357% more evidence for the alternative hypothesis than the null for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 1.194 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.
Prior cumulative density in standardized ROPE [-0.4, 0.4]: 0.05 Posterior cumulative density in standardized ROPE [-0.4, 0.4]: 0.266 H0 Odds: 5.362 H1 Odds: 0.772 There is 594.344% more evidence for the null hypothesis than the alternative for an effect at 0.8 FLAG: Need to gather more evidence for either hypothesis (Scientific Reports standards of BF 10 or 0.1) BF: 0.144 NOTE: BF is the Bayes Factor vs. ROPE, which is the odds of the posterior (H1) falling within the standardized ROPE relative to the odds of the prior (H0). Here, the prior is a mean-centered normal distribution such that the cumulative probability density within the std ROPE is 5%. The posterior is the standardized distribution of difference scores. Also note that the posterior's cumulative probability density within std ROPE is NOT that of the HDI in ROPE. For BF, we evaluate the entirety of the distribution.